Optical element and manufacturing method thereof

ABSTRACT

A hologram that can obtain high diffraction efficiency when reconstructed and is superior in productivity is provided. An arbitrary object image and a recording surface in which representative points are disposed with predetermined pitches are defined by use of a computer. At the position of each individual representative point, a complex amplitude for the wave front of object light emitted from the object image is calculated, and a complex amplitude distribution is calculated on the recording surface. This complex amplitude distribution is expressed by a three-dimensional cell having a groove in the surface thereof. Four kinds of groove depths are defined in accordance with the phase θ, and seven kinds of groove widths are defined in accordance with the amplitude A. Thereby, 28 kinds of three-dimensional cells in total are prepared, and a three-dimensional cell corresponding to the phase θ and amplitude A of the complex amplitude for the representative point is disposed at the position of each representative point. One of the 28 kinds of three-dimensional cells is disposed at the position of each representative point on the recording surface, and thereby a hologram-recording medium is formed as a set of three-dimensional cells. A reconstructed image is obtained by the phase/amplitude modulating function of the groove part of each cell.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to an optical element and amanufacturing method thereof and, more particularly, relates to anoptical element capable of recording a stereoscopic image as a hologramand reconstructing the image, and a manufacturing method thereof.

[0002] A holographic technique is conventionally known as a method forrecording a stereoscopic image on a medium and reconstructing thisimage. A hologram produced by this method is used in various fields,such as ornamental art or anti-counterfeit seals. In order to opticallyproduce the hologram, it is common to record the interference fringebetween object light reflected from an object and reference light on aphotosensitive medium. A laser beam superior in coherence is usuallyused as a light source for the object light and the reference light.Generally, the motion of electromagnetic radiation, such as light, canbe regarded as the propagation of a wave front provided with amplitudeand a phase, and it can be said that the hologram is an optical elementthat functions to reconstruct such a wave front. Therefore, it isnecessary to record information for accurately reconstructing theamplitude and phase of the object light at each position in space on therecording medium of the hologram. If interference fringes generated bythe object light and the reference light are recorded on thephotosensitive medium, information that includes both the phase and theamplitude of the object light can be recorded, and, by projectingillumination reconstructing light equivalent to the reference light ontothe medium, a part of the illumination reconstructing light can beobserved as light provided with a wave front equivalent to the objectlight.

[0003] If the hologram is produced by an optical method using a laserbeam or the like in this way, the phase and amplitude of the objectlight can be recorded only as interference fringes resulting frominterference between the object light and the reference light. Thereason is that the photosensitive medium has a property of beingphotosensitized in accordance with light intensity. On the other hand, atechnique of producing a hologram by computations with use of a computerhas recently been put to practical use. This technique is called a “CGH”(Computer-Generated Hologram) method, in which the wave front of objectlight is calculated by use of a computer, and its phase and itsamplitude are recorded on a physical medium according to a certainmethod so as to produce a hologram. The employment of this computationalholography, of course, enables the recording of an image as interferencefringes between object light and reference light, and, in addition,enables the recording of information for the phase and amplitude of theobject light directly onto a recording surface without using thereference light. For example, a recording method has been proposed inwhich an amplitude is represented by the size of an opening formed in arecording medium whereas a phase is represented by the position of theopening or in which a medium is made up of two recording layers on oneof which an amplitude is recorded and on the other one of which a phaseis recorded.

[0004] The method for recording an image as interference fringes thathas been widely used as an optical hologram producing method is at anadvantage in that productivity is high because, in general, areconstructed image with high resolution can be obtained and because anoptical method is used, but it is at a disadvantage in that an imagedarkens because diffraction efficiency by interference fringes is poorwhen reconstructed. By contrast, the method for recording the phase andamplitude of object light directly onto a medium that has been proposedas one of the computer-generated hologram methods is at an advantage inthat high diffraction efficiency can be obtained, but it is at adisadvantage in that, practically, productivity decreases because therecording of the phase and the amplitude onto the medium is technicallydifficult.

SUMMARY OF THE INVENTION

[0005] It is therefore an object of the present invention to provide anoptical element that can obtain high diffraction efficiency whenreconstructed and that is excellent in productivity.

[0006] (1) The first feature of the present invention resides in anoptical element consisting of a set of a plurality of three-dimensionalcells, wherein:

[0007] a specific amplitude and a specific phase are defined in eachindividual cell,

[0008] and the individual cell has a specific optical property so that,when incident light is provided to the cell, emission light is obtainedby changing an amplitude and a phase of the incident light in accordancewith the specific amplitude and the specific phase defined in the cell.

[0009] (2) The second feature of the present invention resides in theoptical element according to the first feature, wherein each cell has anamplitude-modulating part provided with transmittance corresponding to aspecific amplitude.

[0010] (3) The third feature of the present invention resides in theoptical element according to the first feature, wherein each cell has anamplitude-modulating part provided with reflectivity corresponding to aspecific amplitude.

[0011] (4) The fourth feature of the present invention resides in theoptical element according to the first feature, wherein each cell has anamplitude-modulating part provided with an effective area correspondingto a specific amplitude.

[0012] (5) The fifth feature of the present invention resides in theoptical element according to the first to the fourth features, whereineach cell has a phase-modulating part provided with a refractive indexcorresponding to a specific phase.

[0013] (6) The sixth feature of the present invention resides in theoptical element according to the first to the fourth features, whereineach cell has a phase-modulating part provided with an optical pathlength corresponding to a specific phase.

[0014] (7) The seventh feature of the present invention resides in theoptical element according to the first feature, wherein each cell has aconcave part formed by hollowing a part provided with an areacorresponding to a specific amplitude by a depth corresponding to aspecific phase.

[0015] (8) The eighth feature of the present invention resides in theoptical element according to the first feature, wherein each cell has aconvex part formed by protruding a part provided with an areacorresponding to a specific amplitude by a height corresponding to aspecific phase.

[0016] (9) The ninth feature of the present invention resides in theoptical element according to the seventh or eighth feature, wherein asurface where the concave part or the convex part of each cell is formedserves as a reflecting surface, and incident light provided to the cellis reflected by the reflecting surface and thereby turns into emissionlight.

[0017] (10) The tenth feature of the present invention resides in theoptical element according to the seventh or eighth feature, wherein eachcell includes a main body layer having a concave part or a convex partand a protective layer with which a surface where the concave part orthe convex part of the main body layer is formed is covered, and themain body layer and the protective layer are made of materials differentfrom each other.

[0018] (11) The eleventh feature of the present invention resides in theoptical element according to the tenth feature, wherein the main bodylayer and the protective layer are made of transparent materialsdifferent in a refractive index from each other, and incident lightprovided to the cell passes through the main body layer and theprotective layer and thereby turns into emission light.

[0019] (12) The twelfth feature of the present invention resides in theoptical element according to the tenth feature, wherein a boundarybetween the main body layer and the protective layer forms a reflectingsurface, and incident light provided to the cell is reflected by thereflecting surface and thereby turns into emission light.

[0020] (13) The thirteenth feature of the present invention resides inthe optical element according to the first to the twelfth features,wherein each cell is arranged one-dimensionally or two-dimensionally.

[0021] (14) The fourteenth feature of the present invention resides inthe optical element according to the thirteenth feature, wherein alongitudinal pitch of each cell and a lateral pitch of each cell arearranged so as to be an equal pitch.

[0022] (15) The fifteenth feature of the present invention resides inthe optical element according to the first to the fourteenth features,wherein a complex amplitude distribution of object light from an objectimage is recorded so that the object image is reconstructed whenobserved from a predetermined viewing point so as to be usable as ahologram.

[0023] (16) The sixteenth feature of the present invention resides in amethod for manufacturing an optical element where a predetermined objectimage is recorded, the method comprising:

[0024] a cell defining step of defining a set of a plurality ofthree-dimensional virtual cells;

[0025] a representative-point defining step of defining a representativepoint for each virtual cell;

[0026] an object image defining step of defining an object image to berecorded;

[0027] an amplitude phase defining step of defining a specific amplitudeand a specific phase in each virtual cell by calculating a complexamplitude at a position of each representative point of object lightemitted from the object image; and

[0028] a physical cell forming step of replacing each virtual cell witha real physical cell and forming an optical element that consists of aset of three-dimensional physical cells;

[0029] wherein, at the physical cell forming step, when predeterminedincident light is given to each physical cell, replacement is carriedout by each physical cell having a specific optical property so as toobtain emission light that has changed an amplitude and a phase of theincident light in accordance with a specific amplitude and a specificphase defined in the virtual cell corresponding to the physical cell.

[0030] (17) The seventeenth feature of the present invention resides inthe manufacturing method for the optical element according to thesixteenth feature, wherein at the cell defining step, a cell set isdefined by arranging block-like virtual cells one-dimensionally ortwo-dimensionally.

[0031] (18) The eighteenth feature of the present invention resides inthe manufacturing method for the optical element according to thesixteenth or seventeenth feature, wherein at the amplitude phasedefining step, a plurality of point light sources are defined on theobject image, and object light of a spherical wave having apredetermined amplitude and a predetermined phase is regarded as beingemitted from each point light source, and a totaled complex amplitude ofthe object light from the point light sources at a position of eachrepresentative point is calculated at a predetermined standard time.

[0032] (19) The nineteenth feature of the present invention resides inthe manufacturing method for the optical element according to theeighteenth feature, wherein K point light sources that emit object lightwhose wavelength is λ are defined on the object image, and if anamplitude of object light emitted from a k-th point light source O(k)(k=1 to K) is represented as Ak, and a phase thereof is represented as θk, and a distance between a predetermined representative point P and thek-th point light source O(k) is represented as rk, a totaled complexamplitude of the object light from the K point light sources at thepredetermined representative point P is calculated as follows:

Σ_((k=1,K))(Ak/rk·cos (θ k±2 πrk/λ) +iAk/rk·sin (θ k±2 πrk/λ)).

[0033] (20) The twentieth feature of the present invention resides inthe manufacturing method for the optical element according to thesixteenth to nineteenth features, wherein, at the physical cell formingstep, each virtual cell is replaced with a physical cell having aconcave part formed by hollowing a part provided with an areacorresponding to a specific amplitude by a depth corresponding to aspecific phase.

[0034] (21) The twenty-first feature of the present invention resides inthe manufacturing method for the optical element according to thesixteenth to nineteenth features, wherein, at the physical cell formingstep, each virtual cell is replaced with a physical cell having a convexpart formed by protruding a part provided with an area corresponding toa specific amplitude by a height corresponding to a specific phase.

[0035] (22) The twenty-second feature of the present invention residesin the manufacturing method for the optical element according to thetwentieth or twenty-first feature, wherein:

[0036] a refractive index of a material filled in the concave part ofthe physical cell or a material that constitutes the convex part isrepresented as n1,

[0037] a refractive index of another material in contact with thematerial n1 is represented as n2,

[0038] a wavelength of object light is represented as λ,

[0039] a maximum depth dmax of the concave part or a maximum height dmaxof the convex part is set to be dmax =λ/|n1-n2|,

[0040] a depth or height d corresponding to a specific phase θ isdetermined by the expression d=λ·θ/2(n1-n2)π when n1>n2, and isdetermined by the expression d=dmax -λ·θ/2(n2-n1)π when n1<n2, and

[0041] an object image is reconstructed by transmission light that haspassed through the concave part or the convex part.

[0042] (23) The twenty-third feature of the present invention resides inthe manufacturing method for the optical element according to thetwentieth or twenty-first feature, wherein:

[0043] a refractive index of a material filled in the concave part ofthe physical cell or a material that constitutes the convex part isrepresented as n, a wavelength of object light is represented as λ,

[0044] a maximum depth of the concave part or a maximum height dmax ofthe convex part is set to be dmax=λ/2n,

[0045] a depth or a height d corresponding to the specific phase θ isdetermined by the expression

d=λ·θ/4nπ,

[0046] and

[0047] an object image is reconstructed by reflected light that has beenreflected by the boundary of the concave part or the convex part.

[0048] (24) The twenty-fourth feature of the present invention residesin the manufacturing method for the optical element according to thetwentieth to twenty-third features, wherein α kinds of a plurality ofareas are defined as areas corresponding to a specific amplitude, βkinds of a plurality of depths or heights are defined as depths orheights corresponding to a specific phase so as to prepare α×β kinds ofphysical cells in total, and each virtual cell is replaced with aphysical cell closest in a necessary optical property among saidphysical cells.

[0049] (25) The twenty-fifth feature of the present invention resides inthe manufacturing method for the optical element according to thesixteenth to twenty-fourth features, further comprising aphase-correcting step of correcting the specific phase defined for eachvirtual cell in consideration of a direction of illumination lightprojected when reconstructed or in consideration of a position of aviewing point when reconstructed.

[0050] (26) The twenty-fifth feature of the present invention resides inthe manufacturing method for the optical element according to thesixteenth to twenty-fifth features, wherein:

[0051] at the cell defining step, a cell set of virtual cells arrangedon a two-dimensional matrix is defined by arranging the virtual cellshorizontally and vertically,

[0052] at the amplitude phase defining step, a plurality of M pointlight source rows that are each extended in a horizontal direction andare mutually disposed in a vertical direction are defined on an objectimage, and M groups in total are defined by defining virtual cells thatbelong to a plurality of rows contiguous in the vertical direction inthe two-dimensional matrix as one group,

[0053] the M point light source rows and the M groups are caused tocorrespond to each other in accordance with an arrangement orderrelative to the vertical direction, and

[0054] a totaled complex amplitude at a position of each representativepoint is calculated on a supposition that object light emitted from apoint light source in an m-th point light source row (m=1 to M) reachesonly virtual cells that belongs to an m-th group.

BRIEF DESCRIPTION OF THE DRAWINGS

[0055]FIG. 1 is a perspective view showing general holography foroptically recording an object image as interference fringes by use ofreference light.

[0056]FIG. 2 is a perspective view showing the amplitude and phase ofobject light that has reached a representative point P(x, y) on arecording surface 20 when a point light source O and the recordingsurface 20 are defined.

[0057]FIG. 3 is a perspective view showing the complex amplitude ofobject light at the position of the representative point P(x, y) whenthe object light emitted from each point light source on an object image10 has reached the representative point P(x, y) on the recording surface20.

[0058]FIG. 4 shows the calculation of an amplitude A (x, y) and a phaseθ (x, y) on the basis of a complex amplitude shown by a coordinate pointQ on a complex coordinate plane.

[0059]FIG. 5 is a perspective view showing one example of athree-dimensional virtual cell set 30 defined to record the object image10.

[0060]FIG. 6 shows the function of the amplitude modulation and phasemodulation of a three-dimensional cell C(x, y) used in the presentinvention.

[0061]FIG. 7 shows one example of 16 kinds of physical cells differentin transmittance and in refractive index that are to be the constituentparts of an optical element according to the present invention.

[0062]FIG. 8 is a perspective view showing one example of the structureof a physical cell C(x, y) considered most suitable for use in thepresent invention.

[0063]FIG. 9 is a front view for explaining a reason why amplitudeinformation is recorded as a width G1 of a groove G(x, y) and phaseinformation is recorded as a depth G2 of the groove G(x, y) when thephysical cell C(x, y) shown in FIG. 8 is used as a transmission typecell.

[0064]FIG. 10 is a front view for explaining a reason why amplitudeinformation is recorded as the width G1 of the groove G(x, y) and phaseinformation is recorded as the depth G2 of the groove G(x, y) when thephysical cell C(x, y) shown in FIG. 8 is used as a reflection type cell.

[0065]FIG. 11 is a perspective view showing an example in which sevenkinds of groove widths and four kinds of depths are determined so that28 kinds of physical cells in total are prepared in the structure of thephysical cell C(x, y) shown in FIG. 8.

[0066]FIG. 12 shows the relationship between the refractive index andthe groove depth of each part for the transmission type cell C(x, y).

[0067]FIG. 13 shows the relationship between the refractive index andthe groove depth of each part for the reflection type cell C(x, y).

[0068]FIG. 14 is a side view showing a basic form in whichreconstructing illumination light is projected from a normal directiononto the optical element of the present invention, and an object imagerecorded as a hologram is observed from the normal direction.

[0069]FIG. 15 is a side view showing a form in which reconstructingillumination light is projected from an oblique direction onto theoptical element of the present invention, and an object image recordedas a hologram is observed from the normal direction.

[0070]FIG. 16 is a side view showing a form in which reconstructingillumination light is projected from the normal direction onto theoptical element of the present invention, and an object image recordedas a hologram is observed from the oblique direction.

[0071]FIG. 17 is a side view showing a principle according to whichspecific phase is subjected to corrective processing in order to make anoptical element that corresponds to a reconstructing environment shownin FIG. 15.

[0072]FIG. 18 is a side view showing a principle according to whichspecific phase is subjected to corrective processing in order to make anoptical element that corresponds to a reconstructing environment shownin FIG. 16.

[0073]FIG. 19 is a perspective view showing a technique for making anoptical element that corresponds to a reconstructing environment inwhich white reconstructing illumination light is used.

[0074]FIG. 20 is a perspective view showing an example in whichthree-dimensional cells are arranged like a one-dimensional matrix so asto construct a three-dimensional virtual cell set 30.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0075] The present invention will be hereinafter described on the basisof the embodiments shown in the figures.

[0076] § 1. Basic Principle of the Present Invention

[0077]FIG. 1 is a perspective view that shows general holography inwhich an object image is optically recorded as interference fringes byuse of reference light. When a stereoscopic image of an object 10 isrecorded onto a recording medium 20, the object 10 is illuminated withlight (normally, with a laser beam) having the same wavelength asreference light R, and interference fringes formed by object light fromthe object 10 and the reference light R on the recording medium 20 arerecorded. Herein, if an XY coordinate system is defined on the recordingmedium 20, and attention is paid to an arbitrary point P(x, y) locatedat coordinates (x, y), the amplitude intensity of a composite waveresulting from interference between each object light from each pointO(1), O(2), . . . ,O(k), . . . ,O(K) located on the object 10 and thereference light R will be recorded onto the point P(x, y). Likewise, theamplitude intensity of the composite wave resulting from theinterference between the object light from each point and the referencelight R will be recorded onto another point P(x′,y′) on the recordingmedium 20. However, since a difference in the propagation distance oflight exists, the amplitude intensity recorded onto the point P(x, y)and the amplitude intensity recorded onto the point P(x′,y′) aredifferent from each other. As a result, an amplitude intensitydistribution is recorded onto the recording medium 20, and the amplitudeand phase of the object light are expressed by this amplitude intensitydistribution. When reconstructed, reconstructing illumination lighthaving the same wavelength as the reference light R is projected fromthe same direction as that of the reference light R (or, alternatively,from a direction that has a plane symmetry with respect to the recordingmedium 20), and thus a stereoscopic reconstructed image of the object 10is obtained.

[0078] In order to record interference fringes onto the recording medium20 according to an optical method, a photosensitive material is used asthe recording medium 20, and interference fringes are recorded as alight and dark pattern on the recording medium 20. On the other hand, ifthe computer-generated hologram method is used, a phenomenon occurringin the optical system shown in FIG. 1 requires simulation on a computer.Specifically, the object image 10 and the recording surface 20 aredefined in a virtual three-dimensional space on the computer instead ofthe real object 10 or the real recording medium 20, and many point lightsources O(1), O(2), . . . ,O(k), . . . ,O(K) are defined on the objectimage 10. Further, object light (i.e., spherical wave) with apredetermined wavelength, amplitude, and phase is defined for each pointlight source, and reference light with the same wavelength as the objectlight is defined. On the other hand, many representative points P(x, y)are defined on the recording surface 20, and the amplitude intensity ofa composite wave of both the object light and the reference light thatreach the position of each representative point is calculated. Since anamplitude intensity distribution (i.e., interference fringes) isobtained on the recording surface 20 by computation, a physical hologramrecording medium can be formed if the amplitude intensity distributionis recorded onto the physical recording medium in the form of alight/dark distribution or as a concave/convex distribution.

[0079] In fact, the interference fringes are not necessarily required tobe recorded by using the reference light R if the computer-generatedhologram method is used. It is also possible to record the object lightfrom the object image 10 directly onto the recording surface 20. In moredetail, when a hologram is optically generated, it is necessary togenerate an interference wave on the recording medium 20 made of aphotosensitive material during a fixed period of time needed forexposure and to record this wave as interference fringes. Therefore, itis necessary to generate an interference wave that turns to a standingwave by use of reference light. However, if the computer-generatedhologram method is used, the state of the wave at a certain moment thatexists on the recording surface 20 can be observed in such a way as if alapse in time is stopped, and this wave can be recorded. In other words,the amplitude and phase of the object light at the position of eachrepresentative point on the recording surface 20 at a predeterminedstandard time can be obtained by calculation. In the present invention,this advantage in a computer-generated hologram is employed, and themethod for directly recording the amplitude and phase of the objectlight is used without using the method for recording the object light asinterference fringes resulting from cooperation with the referencelight.

[0080] Now let us consider how the amplitude and phase of the objectlight that has reached the representative point P(x, y) on the recordingsurface 20 are calculated when the point light source O and therecording surface 20 are defined as shown in, for example, theperspective view of FIG. 2. Generally, a wave motion in consideration ofthe amplitude and the phase is expressed by the following function ofcomplex variable (i is an imaginary unit):

A cos θ+i A sin θ

[0081] Herein, A is a parameter showing the amplitude, and θ is aparameter showing the phase. Accordingly, if object light emitted from apoint light source O is defined by the function A cos θ+i A sin θ, theobject light at the position of a representative point P(x, y) isexpressed by the following function of the complex variable:

A/r cos (θ+2 πr/λ)+i A/r sin (θ+2 πr/λ)

[0082] Herein, r is a distance between the point light source 0 and therepresentative point P(x, y), and λ is a wavelength of the object light.The amplitude of the object light attenuates as the distance r becomesgreater, and the phase depends on the distance r and the wavelength λ.This function does not have variables that indicate time. The reason isthat this function is an expression showing the momentary state of awave observed when a lapse in time is stopped at a predeterminedstandard time as described above.

[0083] Accordingly, in order to record information for the object image10 onto the recording surface 20, many point light sources O(1), O(2), .. . , O(k), . . . , O(K) are defined on the object image 10 as shown inthe perspective view of FIG. 3, and then the amplitude and phase of acomposite wave of the object light emitted from each point light sourceare calculated at the position of each representative point on therecording surface 20, and the calculation result is recorded by acertain method. Let us now suppose that K point light sources in totalare defined on the object image 10, and the object light emitted fromthe k-th (“-th” is a suffix indicating an ordinal number) point lightsource O(k) is expressed by the following function of the complexvariable as shown in FIG. 3:

Ak cos θk+i Ak sin θk

[0084] If the object image 10 is constructed of a set of pixels each ofwhich has a predetermined gradation value (concentration value), theparameter Ak showing the amplitude is fixed in accordance with thegradation value of a pixel which exists at the position of the pointlight source O(k). The phase θk is allowed to be defined generally asθk=0. However, it is also possible to create such a setting as to emitobject light rays different in phase from each part of the object image10 if necessary. When the object light expressed by the above functioncan be defined for each of all the K point light sources, the compositewave of all the K object light at the position of an arbitraryrepresentative point P(x, y) on the recording surface 20 is expressed bythe following function of the complex variable as shown in FIG. 3:

Σ_(k=1,K)(Ak/rk cos (θk+2 πrk/λ) +i Ak/rk sin (θk+2 πrk/λ)

[0085] Herein, rk is the distance between the k-th point light sourceO(k) and the representative point P(x, y). The above functioncorresponds to an expression that is used when the object image 10 isreconstructed at the back of the recording medium. When the object image10 is reconstructed to rise to the front side of the recording medium,the function of the complex variable is merely calculated according tothe following expression (note that the reference character in the termof the phase is negative):

Σ_(k=1,K)(Ak/rk cos (θk-2 πrk/λ) +i Ak/rk sin (θk-2 πrk/λ)

[0086] Therefore, the function of the complex variable in considerationof both situations is as follows:

Σ_(k=1,K)(Ak/rk cos (θk±2 πrk/λ) +i Ak/rk sin (θk±2 πrk/λ)

[0087] If the form of Rxy+iIxy is taken under the condition that thereal number part of this function is Rxy and the imaginary number partthereof is Ixy, the complex amplitude (i.e., amplitude in considerationof the phase) at the position of the representative point P(x, y) ofthis composite wave is shown by a coordinate point Q on the complexcoordinate plane as shown in FIG. 4. After all, the amplitude of thecomposite wave of the object light at the representative point P(x, y)is given by the distance A(x, y) between the origin O and the coordinatepoint Q on the coordinate plane shown in FIG. 4, and the phase is givenby the angle θ(x, y) between the vector OQ and the real number axis.

[0088] Thus, the amplitude A(x, y) and phase θ(x, y) of the compositewave of the object light at the position of the arbitrary representativepoint P(x, y) defined on the recording surface 20 is obtained bycomputation. Accordingly, the complex amplitude distribution (i.e.,distribution of the amplitude and phase of the object-light-compositewave) of the object light emitted from the object image 10 is obtainedon the recording surface 20. As a result, the object image 10 can berecorded as a hologram if the complex-amplitude distribution obtained inthis way is recorded on a physical recording medium in some way so thatthe wave front of the object light is to be reconstructed and thenpredetermined reconstructing illumination light is given.

[0089] In order to record a complex amplitude distribution of objectlight emitted from the object image 10 onto the recording surface 20,the present inventor has conceived a method for using three-dimensionalcells. The following procedure should be carried out to record a complexamplitude distribution by use of three-dimensional cells and record theobject image 10 as a hologram. First, a three-dimensional virtual cellset 30 is defined at the position of the recording surface 20 as shownin FIG. 5, for example. The three-dimensional virtual cell set 30 isconstructed by vertically and horizontally arranging block-like virtualcells each of which has a predetermined size so as to place the cellstwo-dimensionally. Thereafter, the representative point of each virtualcell is defined. The position of the representative point may be onearbitrary point in the cell. In this case, the representative point ofthe cell is defined at the position of the center point on the frontsurface of the cell (i.e., surface facing the object image 10). Forexample, if an XY coordinate system is defined on the front surface ofthe three-dimensional virtual cell set 30 (i.e., on the surface facingthe object image 10), and a virtual cell having the representative pointP(x, y) located at the position of coordinates (x, y) in this coordinatesystem is called a virtual cell C(x, y), the representative point P(x,y) will occupy the center point of the front surface of this virtualcell C(x, y).

[0090] On the other hand, the object image 10 is defined as a set ofpoint light sources. In the example of FIG. 5, the object image 10 isdefined as a set of K point light sources O(1), O(2), . . . , O(k), . .. , O(K). Object light having predetermined amplitude and phase isemitted from each point light source, and a composite wave of theseobject light rays reaches the representative point P(x, y). The complexamplitude of this composite wave can be calculated according to theabove-mentioned expressions and can be shown as a coordinate point Q onthe complex coordinate plane shown in FIG. 4, and, based on thiscoordinate point Q, the amplitude A(x, y) and phase θ(x, y) areobtained, as described above. Herein, the amplitude A(x, y) and phaseθ(x, y) obtained for the representative point P(x, y) will be called aspecific amplitude A(x, y) and a specific phase θ(x, y) for the virtualcell C(x, y) including the representative point P(x, y).

[0091] The above-mentioned procedure is practically carried out asarithmetic processing by use of a computer. Accordingly, concerning eachof all the virtual cells that make up the three-dimensional virtual cellset 30, a specific amplitude and a specific phase can be obtained bythis arithmetic processing. Therefore, an optical element (i.e., ahologram recording medium in which the object image 10 is recorded) thatis made up of a set of three-dimensional physical cells can be formed byreplacing these virtual cells with real physical cells, respectively.Herein, the physical cell to be replaced with the virtual cell must haveoptical properties by which the amplitude and phase of incidence lightcan be modulated in accordance with the specific amplitude and specificphase defined in the virtual cell. In other words, when predeterminedincidence light is given, the replaced individual physical cell musthave the specific optical properties of having a function to generateemission light by changing the amplitude and phase of the incidencelight in accordance with the specific amplitude and specific phase thathave been defined in the virtual cell before replacement.

[0092] When predetermined reconstructing illumination light (ideally, aplane wave of monochromatic light with the same wavelength as thewavelength λ of the object light used in the above-mentioned arithmeticprocessing) is projected onto the optical element made up of a set ofphysical cells having the specific optical properties, thereconstructing illumination light is modulated by the specific amplitudeand the specific phase in each physical cell. Therefore, the originalwave front of the object light is reconstructed. As a result, thehologram recorded in this optical element is reconstructed.

[0093] § 2. Concrete Structure of Physical Cell

[0094] Next, the concrete structure of a physical cell used in thepresent invention will be described. A physical cell used in the presentinvention is a three-dimensional stereo-cell, and its specific amplitudeand its specific phase are defined. Any type of cell can be used if ithas such a specific optical property that emission light in which theamplitude and phase of predetermined incidence light are changed inaccordance with the specific amplitude and specific phase defined in thecell can be obtained when the incidence light is given to the cell. Forexample, in a case in which an amplitude A(x, y) and a phase θ(x, y) isrecorded for a three-dimensional cell C(x, y) shown in FIG. 6, andincidence light Lin whose amplitude is Ain and whose phase is θ in isgiven to this cell, all that is needed is to obtain emission light Loutwhose amplitude Aout equals Ain A(x, y) and whose phase θ out equals θin ±θ(x, y). The amplitude Ain of the incidence light undergoesmodulation by the specific amplitude A(x, y) recorded on the cell andchanges into the amplitude Aout, whereas the phase θ in of the incidencelight undergoes modulation by the specific phase θ(x, y) recorded on thecell and changes into the phase θ out.

[0095] One method for modulating the amplitude in the three-dimensionalcell is to provide an amplitude-modulating part having transmittancethat corresponds to the specific amplitude in the cell (the entire cellmay be used as the amplitude-modulating part, or theamplitude-modulating part may be provided to a part of the cell). Forexample, a cell provided with the amplitude-modulating part whosetransmittance is Z% serves as a cell in which the specific amplitude ofA(x, y) equal to Z/100 is recorded, and, when incidence light with theamplitude Ain passes through this cell, it is subjected to amplitudemodulation by emission light whose amplitude Aout equals Ain·Z/100. Onepossible method for setting the transmittance of each three-dimensionalcell at an arbitrary value is to, for example, change the content of acoloring agent for each cell.

[0096] Another method for modulating the amplitude in thethree-dimensional cell is to provide an amplitude-modulating part havingreflectivity that corresponds to the specific amplitude in the cell. Forexample, a cell provided with the amplitude-modulating part whosereflectivity is Z% serves as a cell in which the specific amplitude ofA(x, y) equal to Z/100 is recorded, and, when incidence light with theamplitude Ain is reflected by this amplitude-modulating part and isemitted, it is subjected to amplitude modulation by emission light whoseamplitude Aout equals Ain·Z/100. One possible method for setting thereflectivity of each three-dimensional cell at an arbitrary value is to,for example, prepare a reflecting surface in the cell (this reflectingsurface serves as the amplitude-modulating part) and set thereflectivity of the reflecting surface at an arbitrary value. Morespecifically, the ratio of reflected light to scattered light can beadjusted by, for example, changing the surface roughness of thereflecting surface, and therefore the adjustment of the surfaceroughness makes it possible to prepare a cell having arbitraryreflectivity.

[0097] Still another method for modulating the amplitude in thethree-dimensional cell is to provide an amplitude-modulating part havingan effective area that corresponds to the specific amplitude in thecell. For example, if it is assumed that the area of all the incidentregion of incidence light is 100%, a cell having an amplitude-modulatingpart constructed such that emission light effective for reconstructingan object image can be obtained only from incidence light that hasstruck a part having a Z% effective area thereof serves as a cell inwhich the specific amplitude of A(x, y)=Z/100 is recorded. That is, evenif incidence light having the amplitude Ain strikes theamplitude-modulating part, only Z% of the light goes out as effectiveemission light, and therefore it is subjected to amplitude modulation byemission light having the amplitude of Aout =Ain·Z/100. One possiblemethod for obtaining effective emission light only from a region havingsuch a specific effective area is to use a cell having a physicalconcave/convex structure. A concrete example thereof will be describedin § 3.

[0098] On the other hand, one method for modulating the phase in thethree-dimensional cell is to provide a phase-modulating part having arefractive index that corresponds to the specific phase in the cell (theentire cell can be used as the phase-modulating part, or thephase-modulating part can be provided to a part of the cell). Forexample, even if incidence light with the same phase is given, adifference in the phase of emission light arises between a cell providedwith the phase-modulating part made of a material whose refractive indexis n1 and a cell provided with the phase-modulating part made of amaterial whose refractive index is n2. Therefore, arbitrary phasemodulation can be applied to the incidence light by constructing thecell made of various materials with different refractive indexes.

[0099] Another method for modulating the phase in the three-dimensionalcell is to provide a phase-modulating part having an optical path lengththat corresponds to the specific phase in the cell (the entire cell canbe used as the phase-modulating part, or the phase-modulating part canbe provided to a part of the cell). For example, even if the cell has aphase-modulating part made of the same material whose refractive indexis n, a difference in the phase of each emission light will arise if theoptical path length of the phase-modulating part is different regardlessof the fact that incidence light with the same phase is given. Forexample, if the optical path length of the phase-modulating partprovided in a first cell is L, and the optical path length of thephase-modulating part provided in a second cell is 2L, the distance bywhich emission light emitted from the second cell travels through thematerial whose refractive index is n is twice as long as in the case ofemission light emitted from the first cell even if incidence light withthe same phase is given. Therefore, such a great phase differencearises. A method for realizing a phase-modulating part with an arbitraryoptical path length is to use a cell having a physical concave/convexstructure. A concrete example thereof will be described in § 3.

[0100] A three-dimensional cell having an amplitude modulating functionbased on a specific amplitude or a three-dimensional cell having a phasemodulating function based on a specific phase can be realized by some ofthe methods described above, and an optical element according to thepresent invention can be realized by selecting an arbitrary method fromamong the amplitude modulating methods and the phase modulating methodsmentioned above. For example, if a method in which anamplitude-modulating part with transmittance that corresponds to aspecific amplitude is provided in the cell is employed as the amplitudemodulating method, and a method in which a phase-modulating part with arefractive index that corresponds to a specific phase is provided in thecell is employed as the phase modulating method, and the entire cell isused as the amplitude-modulating part and as the phase-modulating part,an optical element can be formed by selectively arranging 16 kinds ofphysical cells shown in the table of FIG. 7. The horizontal axis of thistable indicates amplitude A, and the vertical axis thereof indicatesphase θ. The amplitude A and the phase θ are each divided into fourranges.

[0101] Herein, the cells (i.e., cells of the first column in the table)depicted in a range in which the amplitude A corresponds to “0-25%” areones that are each made of a material whose transmittance is very low,the cells (i.e., cells of the second column in the table) depicted in arange in which the amplitude A corresponds to “25-50%” are ones that areeach made of a material whose transmittance is slightly low, the cells(i.e., cells of the third column in the table) depicted in a range inwhich the amplitude A corresponds to “50-75%” are ones that are eachmade of a material whose transmittance is slightly high, and the cells(i.e., cells of the fourth column in the table) depicted in a range inwhich the amplitude A corresponds to “75-100%” are ones that are eachmade of a material whose transmittance is very high. On the other hand,the cells (i.e., cells of the first row in the table) depicted in arange in which the phase θ corresponds to “0-π/2” are ones that are eachmade of a material whose refractive index n1 is very close to that ofair, the cells (i.e., cells of the second row in the table) depicted ina range in which the phase 0 corresponds to “π/2-π” are ones that areeach made of a material whose refractive index n2 is slightly greaterthan that of air, the cells (i.e., cells of the third row in the table)depicted in a range in which the phase θ corresponds to “π-3 π/2” areones that are each made of a material whose refractive index n3 is muchgreater than that of air, and the cells (i.e., cells of the fourth rowin the table) depicted in a range in which the phase θ corresponds to “3π/2-2 π” are ones that are each made of a material whose refractiveindex n4 is very much greater than that of air.

[0102] In the example of FIG. 7, sixteen cells in total with four kindsof transmittances and four kinds of refractive indexes are prepared asdescribed above. A desirable way of recording the amplitude and phase inthe cell with higher accuracy is to set the transmittance steps and therefractive-index steps in more detail and prepare even more kinds ofcells. What is needed to replace the virtual cells by use of thesesixteen kinds of physical cells is to select a physical cell that hasoptical properties closest in the optical properties needed to carry outmodulation based on the specific amplitude and the specific phasedefined in each virtual cell.

[0103] § 3. Practical Structure of Physical Cell

[0104] If physical cells used in the present invention are cells thathave a function to modulate incidence light in accordance with aspecific amplitude and a specific phase as described above, any kind ofcell structure is allowed to embody the present invention. FIG. 7 showsan example in which the modulation according to a specific amplitude iscontrolled by the transmittance, and the modulation according to aspecific phase is controlled by the refractive index. Theoretically,many methods exist to modulate the amplitude or the phase as describedabove. However, from the viewpoint of industrial mass production, allthe methods are not necessarily practical. In order to reconstruct anobject image that has a certain degree of resolution by using theoptical element according to the present invention, the size of eachthree-dimensional cell must be determined to be less than a criterion(roughly speaking, when the size of a cell exceeds 100 μm, it isdifficult to reconstruct a satisfactorily discernible object image).Therefore, it is need to two-dimensionally arrange small cells as acomponent if sixteen kinds of physical cells shown in FIG. 7 arecombined to form an optical element, and, additionally, there is a needto dispose a specific cell of the sixteen kinds of cells at a specificposition. From this fact, it can be found that the method forconstructing the optical element using the physical cells shown in FIG.7 is unsuitable for industrial mass production.

[0105] As a method in which amplitude information and phase informationcan be given to a single physical cell and an optical element suitablefor industrial mass production is constructed with a set of suchphysical cells, the present inventor has contrived a method for giving aconcave/convex structure to each physical cell, then recording amplitudeinformation as the area of this concave/convex structure part, andrecording phase information as a level difference (i.e., depth of aconcave part or height of a convex part) in the concave/convex structurepart.

[0106]FIG. 8 is a perspective view showing an example of the structureof a physical cell C(x, y) that can be regarded as most suitable for usein the present invention. As shown in the figure, this three-dimensionalphysical cell has an almost rectangular solid block shape, and a grooveG(x, y) is formed in the upper surface thereof. In this example, thesize of the physical cell C(x, y), C1=0.6 μm, C2=0.25 μm, and C3=0.25μm, and the size of the groove G(x, y), G1=0.2 μm, G2=0.05 μm, andG3=C3=0.25 μm are shown in the figure. The use of the thus constructedphysical cell C(x, y) makes it possible to record the amplitudeinformation as a value of the lateral width G1 of the groove G(x, y) andrecord the phase information as a value of the depth G2 of the grooveG(x, y). In other words, when a virtual cell in which a specificamplitude and a specific phase are defined is replaced with the thusconstructed physical cell, the replacement is carried out by thephysical cell having the size G1 corresponding to the specific amplitudeand having the size G2 corresponding to the specific phase.

[0107] With reference to the front view of FIG. 9, a description will beprovided of the reason why the amplitude information is recorded as thewidth G1 of the groove G(x, y) and the phase information is recorded asthe depth G2 of the groove G(x, y) in the physical cell shown in FIG. 8.Let us now suppose that the physical cell C(x, y) is made of a materialwith the refractive index n2, and the part outside the physical cellC(x, y) is made of a material (e.g., air) with the refractive index n1.In this case, when the optical path length passing through the mediumwith the refractive index n2 is compared between incident light L1 thathas struck vertically the inner surface S1 of the groove G(x, y) andincident light L2 that has struck vertically the outer surface S2 of thegroove G(x, y), it can be found that the optical path length of thelight L1 is shorter than that of the light L2 by the depth G2 of thegroove G(x, y). Therefore, if the refractive indexes n1 and n2 aredifferent from each other, a predetermined phase difference will arisebetween the light L1 and the light L2 emitted from the physical cellC(x, y) as transmission light.

[0108] On the other hand, FIG. 10 is a front view showing a case inwhich emission light is obtained as reflected light from the physicalcell C(x, y). In this example, the upper surface of the physical cellC(x, y), i.e., surfaces S1 and S2 are reflecting-surfaces, and theincident light L1 that has struck almost vertically the inner surface S1of the groove G(x, y) and the incident light L2 that has struck almostvertically the outer surface S2 of the groove G(x, y) are reflected bythe respective surfaces almost vertically and emitted therefrom. At thistime, it can be found that, when the entire optical path length alongthe path of the incidence and reflection is compared, the optical pathlength of the light L1 becomes longer than that of the light L2 bydouble the depth G2 of the groove G(x, y). Therefore, a predeterminedphase difference arises between the light L1 and the light L2 emittedfrom the physical cell C(x, y) as reflected light.

[0109] Accordingly, even if the physical cell C(x, y) is a transmissiontype cell or a reflection type cell, a predetermined phase differencearises between the incident light L1 that has struck the inner surfaceS1 of the groove G(x, y) and the incident light L2 that has struck theouter surface S2 of the groove G(x, y). This phase difference depends onthe depth G2 of the groove G(x, y). Therefore, if only the emissionlight obtained on the basis of the incidence light that has struck theinner surface Si of the groove G(x, y) among the incident light raysthat have struck the upper surface of the physical cell C(x, y) istreated as emission light effective for the reconstruction of the objectimage 10 (in other words, if only the light L1 is treated as emissionlight effective for the reconstruction of the image in FIG. 9 or FIG.10), emission light L1 effective for the image reconstructionresultantly undergoes phase modulation by a specific phase thatcorresponds to the depth G2 of the groove G(x, y) in this physical cellC(x, y). Thus, the phase information of the object light can be recordedas the depth G2 of the groove G(x, y).

[0110] Further, if only the emission light obtained on the basis of theincidence light that has struck the inner surface S1 of the groove G(x,y) is treated as emission light effective for the reconstruction of theobject image 10 as mentioned above, the amplitude information of theobject light can be recorded as the width G1 of the groove G(x, y). Thereason is that the area of the inner surface Si of the groove G(x, y)enlarges, and the percentage of the emission light effective for thereconstruction of the object image 10 increases as the width Gi of thegroove G(x, y) becomes greater. That is, since the emission light L2shown in FIG. 9 or FIG. 10 does not include any significant phasecomponents, the emission light is merely observed as a noise componentof a so-called background, and is not recognized as light effective forreconstructing a significant image even if the emission light L2 isobserved at a viewing position when reconstructed. By contrast, sincethe emission light L1 includes significant phase components, it isobserved as a signal component effective for image reconstruction. Afterall, the width G1 of the groove G(x, y) becomes a factor for determiningthe ratio of the light L1 observed as a signal component among the lightrays emitted from the physical cell C(x, y), and becomes a parameter forgiving the amplitude information of the signal wave.

[0111] Generally, the amplitude information is not expressed by thewidth G1 of the groove G(x, y), but by the area of the inner surface S1of the groove G(x, y). In the embodiment shown in FIG. 8, since thelength G3 of the groove G(x, y) happens to be set to be always equal tothe length C3 of the physical cell C(x, y), the area of the innersurface S1 of the groove G(x, y) is proportional to the extent of thewidth G1. However, the length G3 of the groove G(x, y) does notnecessarily need to be fixed, and both of the width and the length maybe changed so that the area of the inner surface S1 of the groove G(x,y) has variations.

[0112] If a part having an area corresponding to the specific amplitude(i.e., a part corresponding to the surface S1 of FIG. 8) of the uppersurface of the block-like physical cell is hollowed by the depthcorresponding to the specific phase (i.e., depth corresponding to thedimension G2 of FIG. 8) so as to form a concave part (i.e., groove G(x,y)) in this way, the amplitude modulation corresponding to the specificamplitude and the phase modulation corresponding to the specific phasecan be applied to reconstructing illumination light by the thusconstructed physical cell. Even if a convex part, instead of the concavepart, is formed on the block-like physical cell, similar modulationprocessing can be applied. That is, even if the dimension G2 is set at anegative value, and a projection instead of the groove is formed on thephysical block shown in FIG. 8, it is possible to produce an opticalpath difference corresponding to the height of the projection andproduce a phase difference. In other words, if a part having an areacorresponding to the specific amplitude of the upper surface of theblock-like physical cell is protruded by the height corresponding to thespecific phase so as to form a convex part, the amplitude modulationcorresponding to the specific amplitude and the phase modulationcorresponding to the specific phase can also be applied toreconstructing illumination light by the thus constructed physical cell.

[0113] The width G1 and depth G2 of the groove can be consecutivelychanged in the physical cell C(x, y) having the groove G(x, y) shown inFIG. 8, and therefore, theoretically, infinite kinds of physical cellscan be prepared. The use of the infinite kinds of physical cells makesit possible to replace the virtual cell with the physical cell havingthe accurate groove width G1 corresponding to the specific amplitude andthe accurate depth G2 corresponding to the specific phase that aredefined in the virtual cell. However, practically, it is preferable topredetermine α kinds of groove widths and β kinds of depths so as toprepare α×β kinds of physical cells in total and then select a physicalcell closest in necessary optical properties from among the physicalcells. FIG. 11 is a perspective view showing an example in which sevenkinds of groove widths and four kinds of depths are determined so as toprepare 28 kinds of physical cells in total. Each of the 28 kinds ofphysical cells is a block-like physical cell formed as shown in FIG. 8,and, in FIG. 11, the physical cells are arranged in the form of a matrixof four rows and 7 columns.

[0114] In FIG. 11, the seven columns of the matrix indicate thevariation of amplitude A, and the four rows thereof indicate thevariation of phase θ. For example, the cell located at column W1 is acell corresponding to the minimum value of amplitude A, wherein groovewidth G1=0, i.e., a groove G is not formed at all. Rightward, i.e.,toward columns W2 to W7, the cells correspond to greater amplitude A,and the groove width G1 thereof gradually becomes greater. The celllocated at column W7 is a cell corresponding to the maximum value ofamplitude A, wherein groove width G1=cell width C1, i.e., the entiresurface thereof is hollowed. Further, when attention is paid to the rowsof the matrix of FIG. 11, the cell located at row V1, for example, is acell corresponding to the minimum value of phase θ, wherein groove depthG2=0, i.e., a groove G is not formed at all. Downward, i.e., toward rowsV2 to V4, the cells correspond to greater phase θ, and the groove depthG2 thereof gradually becomes greater.

[0115] § 4. Optical Element Manufacturing Method by Use of PracticalPhysical Cells

[0116] Now, a description will be provided of a concrete method formanufacturing an optical element (hologram-recording medium) where anobject image 10 is recorded by use of 28 kinds of physical cells shownin FIG. 11. First, as shown in FIG. 5, the object image 10 formed by aset of point light sources and a three-dimensional virtual cell set 30are defined by use of a computer. Herein, respective virtual cells thatmake up the three-dimensional virtual cell set 30 are block-like cells(at this moment, a groove has not yet been formed) as shown in FIG. 8,and the three-dimensional virtual cell set 30 is formed by arranging thecells two-dimensionally and with equal pitches vertically andhorizontally. The dimension of one virtual cell should be, for example,C1=0.6 μm, C2=0.25 μm, and C3=0.25 μm or so. In this case, if thelateral pitch of the cell is 0.6 μm, and the longitudinal pitch is 0.25μm, the cells can be disposed without any gap. Of course, thedimensional value of each cell shown here is one example, and, inpractice, it is possible to set it at an arbitrary dimension ifnecessary. However, as the cell dimension becomes greater, the visualangle by which a reconstructed image of an object is obtained isnarrowed, and the resolution of the object is lowered proportionately.Reversely, as the cell dimension becomes smaller, the processing offorming a concave/convex structure of the physical cell technicallybecomes difficult. In consideration of the arithmetic processing or theconvenience of the processing of the physical cells, it is preferable todispose the cells with predetermined equal pitches vertically andhorizontally though they do not necessarily need to be disposed withequal pitches.

[0117] After the definition of the object image 10 and the definition ofthe three-dimensional virtual cell set 30 are completed, arepresentative point is defined in each virtual cell, and then thecomplex amplitude of the composite wave of each object light that hasreached each representative point is calculated as described in § 2, anda specific amplitude and a specific phase are defined for each virtualcell. Thereafter, each virtual cell is replaced with any one of the 28kinds of physical cells shown in FIG. 11 (in other words, it is replacedwith a physical cell closest in optical properties needed for modulationaccording to the specific amplitude and the specific phase defined ineach individual virtual cell), and an optical element is formed as a setof physical cells. At this time, the groove-forming surface of eachphysical cell (in the case of the physical cell shown in FIG. 8 or FIG.11, the upper surface) is designed to face the front surface (i.e., thesurface facing the object image 10) of the three-dimensional virtualcell set 30 shown in FIG. 5.

[0118] In fact, the replacement of the virtual cell with the physicalcell is carried out as the processing of forming a given concave/convexstructure on the surface of a medium to become an optical element. Sincethe physical cell is disposed so that its groove is directed forwardwhen each virtual cell of the three-dimensional virtual cell set 30shown in FIG. 5 is replaced with the physical cell as mentioned above, afinally formed optical element appears as a medium whose surface has aconcave/convex structure formed with many grooves. Therefore, thereplacement of the virtual cell with the physical cell is carried out asprocessing of providing data relative to a concave/convex pattern to adrawing device from a computer that stores information for each virtualcell (i.e., information that shows the specific amplitude and thespecific phase defined in each virtual cell) and then drawing theconcave/convex pattern onto the physical surface of the medium by thedrawing device. The processing of drawing a fine concave/convex patterncan be carried out by, for example, a patterning technique that uses anelectron-beam drawing device. What is needed to mass-produce the sameoptical element is to form an original plate in which a desiredconcave/convex structure is formed by the drawing processing that usesan electron-beam drawing device, for example, and to transfer theconcave/convex structure onto many mediums by the stamping step thatuses the original plate.

[0119] The optical element according to the present invention isbasically formed with a main body layer that is obtained bytwo-dimensionally arranging the physical cells shown in FIG. 8. However,a protective layer may be placed on the surface of the main body layerif necessary. This protective layer serves to cover the concave/convexsurface formed in the surface of the main body layer. The main bodylayer and the protective layer are made of materials different from eachother.

[0120] In a transmission type optical element in which incidence lightgiven to each physical cell passes through the main body layer and theprotective layer and then turns into emission light, the main body layerand the protective layer must be made of a transparent material andanother transparent material, respectively, that are different in therefractive index. Here, let us consider a concrete relationship betweenthe depth of the groove G and the phase when a transmission type opticalelement (i.e., transmission type physical cell) of a two-layer structuremade of such a main body layer and a protective layer is manufactured.

[0121] Now, let us consider a transmission type cell C(x, y) having astructure shown in the sectional view of the upside of FIG. 12. This isa cell having a two-layer structure made of a main body layer Ca inwhich a groove G whose depth is d(x, y) is formed and a protective layerCb placed on the upper surface thereof in such a way as to fill thegroove G. Herein, the refractive index of a material that forms theprotective layer Cb (in other words, the refractive index of a materialwith which the concave part is filled or a material that constitutes theconvex part) is represented as n1, and the refractive index of amaterial that forms the main body layer Ca is represented as n2. If themaximum depth dmax of the groove G (in other words, the maximum depth ofthe concave part or the maximum height of the convex part) is set to bedmax=λ/|n1-n2|, a physical cell can be realized in which phasemodulation within the range of 0 through 2 π can be applied to lightwhose wavelength is λ. For example, if the wavelength λ equals 400 nm(λ=400 nm) and the difference |n1-n2| in the refractive index equals 2,the maximum depth can be set to be dmax=200 nm (0.2 μm).

[0122] In this case, as shown in FIG. 12, the depth d(x, y)corresponding to the specific phase θ(x, y) can be obtained by thefollowing equations:

[0123] If n1>n2,

d(x, y)=λ·θ(x, y)/2(n1−n2)π

[0124] and, if n1<n2,

d(x, y)=dmax−λ·θ(x, y)/2(n2−n1)π

[0125] Accordingly, after the specific amplitude and specific phase of acertain virtual cell C(x, y) are obtained as A(x, y) and θ(x, y),respectively, the specific phase θ(x, y) is substituted for the aboveequation so as to calculate a corresponding depth d(x, y), and then aphysical cell that has a depth closest to the resulting depth d(x, y)and has a width closest to the dimension corresponding to the specificamplitude A(x, y) is selected from among the 28 kinds of physical cellsshown in FIG. 11, and the replacement of the virtual cell C(x, y) withthe selected physical cell is carried out. If the protective layer Cb isnot provided, the refractive index of air (almost 1) can be used as therefractive index n1 of the protective layer.

[0126] On the other hand, let us consider a reflection type cell C(x, y)having a structure shown in the sectional view of the upside of FIG. 13.This is a cell having a two-layer structure made of a main body layer Cα in which a groove G whose depth is d(x, y) is formed and a protectivelayer C β placed on the upper surface thereof in such a way as to fillthe groove G. In this cell, the boundary between the main body layer C αand the protective layer C β serves as a reflecting surface. Thereflectance on this reflecting surface is not necessarily to be 100%.The reflecting surface may be a half-mirror having a reflectance of e.g.50%. The reflecting surface is also provided by inserting a halftransparent layer such as a transflector between the main body layer C αand the protective layer C β. Incidence light that has struck theprotective layer C β from the upper side of the figure downward isreflected by the reflecting surface and is emitted upward in the figure.Herein, the refractive index of a material that forms the protectivelayer C β (in other words, the refractive index of a material with whichthe concave part is filled or a material that constitutes the convexpart) is represented as n. If the maximum depth dmax of the groove G (inother words, the maximum depth of the concave part or the maximum heightof the convex part) is set to be dmax=λ/2n, a physical cell can berealized in which phase modulation within the range of 0 through 2 π canbe applied to light whose wavelength is λ. For example, if thewavelength λ equals 400 nm (λ=400 nm) and the refractive index equals 2(n=2), the maximum depth can be set to be dmax=100 nm (0.1 μm).

[0127] In this case, as shown in FIG. 13, the depth d(x, y)corresponding to the specific phase θ(x, y) is obtained by the followingequation:

d(x, y)=λ·θ(x, y)/4n π

[0128] If the protective layer C β is not provided, the refractive indexof air (almost 1) can be used as the refractive index n of theprotective layer. Accordingly, the maximum depth of the groove G can beset to be dmax=λ/2, and the depth d(x, y) corresponding to the specificphase θ(x, y) can be determined by the following equation:

d(x, y)=λ·θ(x, y)/4 π

[0129] § 5. Modification in Consideration of Convenience ofReconstructive Environment

[0130] Let us now consider an environment in which reconstructingillumination light is projected onto the optical element manufacturedaccording to the method described above so as to reconstruct the objectimage 10 recorded as a hologram. FIG. 14 is a side view showing therelationship among an optical element 40 (i.e., hologram-recordingmedium that uses physical cells), reconstructing illumination light Ltor Lr, and a viewing point E that are used for the reconstruction. Ifthe optical element 40 is a transmission type element that usestransmission type cells, the reconstructing illumination light Lt isprojected to the surface opposite to the viewing point E as shown in thefigure, and light that has passed through the optical element 40 isobserved at the viewing point E. If the optical element 40 is areflection type element that uses reflection type cells, thereconstructing illumination light Lr is projected to the surface on thesame side as the viewing point E as shown in the figure, and light thathas been reflected from the optical element 40 is observed at theviewing point E. In any case, when the optical element 40 ismanufactured according to the above method, the most excellentreconstructed image can be obtained in the condition that thereconstructing illumination light Lt or Lr is given as a plane wave ofmonochromatic light and projected in the normal direction to therecording surface (i.e., a two-dimensional array surface on whichphysical cells are arranged) of the optical element 40 as shown in FIG.14 (in other words, reconstructing illumination light is projected sothat the wave front becomes parallel with the recording surface of theoptical element 40), and the image is observed in the normal directionto the recording surface.

[0131] However, the actual reconstructive environment of the opticalelement 40 where the object image 10 is recorded as a hologram does notnecessarily lead to the ideal environment shown in FIG. 14. Especially,in the case of the reflection type, since a head of an observing personis located at the position of the viewing point E, a shadow of theperson, which makes the excellent reconstruction impossible, appears onthe optical element 40 even if the reconstructing illumination light Lris projected from the direction shown in FIG. 14. Therefore, generally,the actual reconstructive environment has an aspect in which thereconstructing illumination light Lt or Lr is projected in the obliquedirection with respect to the recording surface of the optical element40 so as to observe the reconstructed image at the viewing point Elocated in the normal direction as shown in FIG. 15, or, alternatively,an aspect in which the reconstructing illumination light Lt or Lr isprojected in the normal direction to the recording surface of theoptical element 40 so as to observe the reconstructed image at theviewing point E located in the oblique direction as shown in FIG. 16,or, alternatively, an aspect in which both the projecting direction ofthe reconstructing illumination light Lt or Lr and the observingdirection with respect to the viewing point B are set as the obliquedirection.

[0132] What is needed to manufacture the optical element 40 by which anexcellent reconstructed image can be obtained in the actualreconstructive environment is to carry out phase-correcting processingin which the specific phase defined for each virtual cell is corrected,in consideration of the direction of the illumination light projectedwhen reconstructed and the position of the viewing point whenreconstructed.

[0133] For example, let us consider a case in which, as shown in FIG.17, reconstructing illumination light rays L1 through L4 are projectedin the oblique direction, and light rays LL1 through LL4 that haveundergone modulation of the amplitude and the phase as a result ofpassing through the optical element 40 (in other words, light rays LL1through LL4 have the reconstructed wave front of the object lightemitted from the object image 10) are observed at the viewing point Elocated in the normal direction. If the reconstructing illuminationlight rays L1 through L4 are each a monochrome plane wave whosewavelength is A and if the reconstructing illumination light isprojected onto the optical element 40 in the oblique direction, anoptical path difference will have already arisen when the light reacheseach point P1 through P4 on the optical element 40, and incidence lightat each point P1 through P4 will have already generated a phasedifference. For example, the incidence light rays upon the positions ofpoints P2, P3, and P4 are longer in the optical path length by d2, d3,and d4, respectively, than the incidence light ray upon the position ofpoint P1. Therefore, the incidence light has already generated a phasedifference in proportion to the optical path difference. Therefore, ifthere is the supposition that “the optical element 40 is manufactured bywhich an excellent reconstructed image can be obtained in thereconstructive environment shown in FIG. 17”, the specific phase abouteach virtual cell can be calculated according to the above-mentionedmethod, and thereafter the processing of correcting each specific phasecan be carried out in accordance with the position of the cell. Forexample, there is no need to correct the cell located at the position ofpoint P1 of FIG. 17, and the cell located at the position of point P2undergoes the correction of the specific phase so as to cancel a phasedifference caused by the optical path difference d2. Accordingly, if theoptical element 40 is manufactured while carrying out the correction ofthe specific phase, an excellent reconstructed image can be given by thelight rays LL1 through LL4 emitted toward the viewing point E.

[0134] This corrective processing to the specific phase is likewisecarried out in a case in which, as shown in FIG. 18, the reconstructingillumination light rays L1 through L4 are projected in the normaldirection so as to observe the light rays LL1 through LL4 that haveundergone modulation of the amplitude and the phase as a result ofpassing through the optical element 40 (i.e., light that hasreconstructed the wave front of the object light from the object image10) at the viewing point E located in the oblique direction. That is, ifthe reconstructing illumination light rays L1 through L4 are each amonochrome plane wave whose wavelength is λ and if the reconstructingillumination light rays are projected onto the optical element 40 in thenormal direction, no optical path difference occurs when the light rayreaches each point P1 through P4 on the optical element 40, and thephases of the incidence light rays upon points P1 through P4 coincidewith each other. However, a difference arises among the optical pathlengths from points P1 through P4 to the viewing point E that theemission light emitted therefrom reaches, and a phase difference willarise when observed at the viewing point E. For example, the emissionlight rays from the positions of points P2, P3, and P4 are longer in theoptical path length by d2, d3, and d4, respectively, than the emissionlight ray from the position of point P1. Therefore, the emission lighthas generated a phase difference in proportion to the optical pathdifference at the position of the viewing point E. Therefore, if thereis the supposition that “the optical element 40 is manufactured by whichan excellent reconstructed image can be obtained in the reconstructiveenvironment shown in FIG. 18”, the specific phase about each virtualcell can be calculated according to the above-mentioned method, andthereafter the processing of correcting each specific phase can becarried out in accordance with the position of the cell. For example,there is no need to correct the cell located at the position of point P1of FIG. 18, and the cell located at the position of point P2 undergoesthe correction of the specific phase so as to cancel a phase differencecaused by the optical path difference d2. Accordingly, if the opticalelement 40 is manufactured while carrying out the correction of thespecific phase, an excellent reconstructed image can be provided by thelight rays LL1 through LL4 emitted toward the viewing point E.

[0135] The corrective processing to the specific phase for thetransmission type optical element 40 was described above. The sameprinciple of the corrective processing applies to the reflection typeoptical element 40.

[0136] On the other hand, concerning the wavelength of thereconstructing illumination light, a case where monochromatic lightwhose wavelength is λ can be used as reconstructing illumination lightis extremely rare in the actual reconstructive environment, andtherefore, normally, a case where the reconstruction is carried outunder reconstructing illumination light close to white can be regardedas general. If the reconstruction is carried out by use ofreconstructing illumination light that includes a plurality ofwavelength components, different phase modulation is performed for lighthaving each individual wavelength, and therefore an excellentreconstructed image cannot be obtained. Concretely, a reconstructedimage is formed as if images with various colors are superimposed oneach other with slight incongruity.

[0137] Therefore, in order to obtain a fairly excellent reconstructedimage even in the reconstructive environment that uses whitereconstructing illumination light, a method, such as that shown in FIG.19, should be applied when a complex amplitude distribution of objectlight is calculated. Like the system shown in FIG. 5, a system shown inFIG. 19 is used to define the object image 10 and the three-dimensionalvirtual cell set 30 on a computer and calculate for obtaining adistribution of the totaled complex amplitude of each object lightemitted from the object image 10 on the three-dimensional virtual cellset 30. Herein, the three-dimensional virtual cell set 30 is constructedby arranging virtual cells horizontally and vertically, and is a cellset that consists of the virtual cells arranged on the two-dimensionalmatrix. Representative points are defined in the virtual cells,respectively.

[0138] When the technique described herein is employed, the totaledcomplex amplitude at the position of each representative point iscalculated by the following method. First, a plurality of Mpoint-light-source rows each of which extends horizontally and which aremutually arranged vertically are defined on the object image 10. In theexample of the figure, M=3, and three point light source rows m1, m2,and m3 are defined. Each point light source row includes a plurality ofpoint light sources arranged horizontally. For example, a point lightsource row m1 includes j point light sources O(m1,1), O(m1,2), . . . ,O(m1,j). On the other hand, on the side of the three-dimensional virtualcell set 30, M groups in total are defined by defining groups of virtualcells that belong to a plurality of rows contiguous vertically as onegroup in the two-dimensional matrix. In the example of the figure, threegroups in total are defined as M=3. That is, a first group g1 consistsof virtual cells that belong to first through third rows, a second groupg2 consists of virtual cells that belong to fourth through sixth rows,and a third group g3 consists of virtual cells that belong to sevenththrough ninth rows.

[0139] The M point light source rows are thus defined on the side of theobject image 10, and the M groups are defined on the side of thethree-dimensional virtual cell set 30. Thereafter, the M point lightsource rows and the M groups are caused to correspond to each other inaccordance with the arrangement order concerning the vertical direction.That is, in the example of the figure, the uppermost point light sourcerow m1 is caused to correspond to the uppermost group g1, the middlepoint light source row m2 is caused to correspond to the middle groupg2, and the lowermost point light source row m3 is caused to correspondto the lowermost group g3. Thereafter, on the supposition that theobject light emitted from a point light source in the m-th point lightsource row (m=1 to M) reaches only the virtual cell that belongs to them-th group, the totaled complex amplitude at the position of eachrepresentative point is calculated. For example, the object lightemitted from the point light sources O(m1,1), O(m1,2), . . . , O(m1,j)that belong to the point light source row m1 in FIG. 19 is regarded asreaching only the virtual cells that belongs to the group g1 (virtualcells arranged in the first to third rows), and as not reaching thevirtual cells that belongs to the groups g2 and g3, and the totaledcomplex amplitude is calculated. In other words, the calculation of thetotaled complex amplitude at the position of the representative point ofthe virtual cell that belongs to the group g1 is carried out inconsideration of only the object light emitted from the point lightsources O(m1,1), O(m1,2), . . . , O(m1,j) that belong to the point lightsource row m1, not in consideration of the object light emitted from thepoint light sources that belong to the point light source rows m2 andm3.

[0140] Actually, the object image 10 cannot be recorded as an originalhologram if it is recorded under these conditions. After all, the basicprinciple of the hologram resides in that all information for the objectimage 10 is recorded onto any places of the recording surface, andthereby a stereoscopic image can be reconstructed. If the object image10 is recorded under the conditions mentioned above, only information ofa part of the point-light-source row m1 (i.e., part of the upper portionof the object image 10) is recorded in the area of the group g1. As aresult, a stereoscopic reconstructed image as an original hologramcannot be obtained. Concretely, stereoscopic vision relative to thehorizontal direction can be given, but stereoscopic vision relative tothe vertical direction becomes insufficient. However, if the objectimage 10 is recorded under these conditions, a more excellentreconstructed image (i.e., an even clearer reconstructed image includingthe fact that the stereoscopic vision relative to the vertical directionis insufficient) can be obtained in the reconstructive environment thatuses white reconstructing illumination light. The reason is that,whenreconstructed, an effect to control the wavelength distribution of thereconstructing light concerning with the vertical direction can beobtained by recording the object image 10 in such a way as to divide itinto parts concerning with the vertical direction.

[0141] The present invention was described on the basis of theembodiments shown in the figures. However, the present invention is notlimited to these embodiments, and can be carried out in various forms.For example, in the above embodiment, the three-dimensional virtual cellset 30 is defined by arranging three-dimensional cells like atwo-dimensional matrix. However, it is also possible to define thethree-dimensional virtual cell set 30 by preparing three-dimensionalcells that are slender in the horizontal direction as shown in FIG. 20and arranging the three-dimensional cells like a one-dimensional matrix.In the example of FIG. 20, cells C(1), C(2), C(3), . . . , which areslender in the horizontal direction, are arranged in the verticaldirection so as to form the three-dimensional virtual cell set 30. Ifthe object image 10 is recorded onto an optical element that consists ofcells arranged like a one-dimensional matrix in this way, only thereconstructed image in which only the stereoscopic vision relative tothe vertical direction can be given will be obtained, but this issatisfactorily useful depending on its usage.

[0142] The optical element according to the present invention, ofcourse, can be used as a “hologram-recording medium” in which someobject image 10 is recorded as a hologram, and then is reconstructed asa stereoscopic image. However, the present invention is not limited tousage as the hologram-recording medium, and can also be applied to acase in which a general optical element, such as an optical filter, apolarized light element, or a light modulating element, is manufactured.For example, if a pattern of a simple lattice design is used as theobject image 10, and a complex amplitude distribution of object lightemitted from this pattern is recorded onto a physical medium, an opticalelement with peculiar optical properties can be realized.

[0143] Further, the three-dimensional cells are not necessarily neededto be arranged along a rectangular coordinate system. For example, theycan also be arranged along a spherical surface by use of a polarcoordinate system. Additionally, the three-dimensional physical cellsused in the above embodiments are cells serving as passive elements.However, the physical cells used in the present invention may beconstructed by active elements capable of controlling the refractiveindex, transmittance, reflectivity, etc., on the basis of a signal fromthe outside. For example, if each individual physical cell is made of abirefringent material like a liquid crystal, and the ratio of anordinary ray to an extraordinary ray is controlled according to anoutside signal, the specific amplitude and specific phase of thephysical cell can be determined on the basis of a signal given from theoutside. In the optical element that uses the active element as aphysical cell, since a recorded image is not physically fixed, anarbitrary object image can be reconstructed in accordance with a signalfrom the outside.

[0144] As described above, according to the present invention, highdiffraction efficiency can be obtained when reconstructed since anobject image is recorded as a complex amplitude distribution of objectlight, not as interference fringes. Moreover, since the complexamplitude distribution is recorded while employing the opticalproperties of a three-dimensional cell, an optical element superior inproductivity can be provided.

What is claimed is:
 1. An optical element consisting of a set of aplurality of three-dimensional cells, wherein: a specific amplitude anda specific phase are defined in each individual cell, and saidindividual cell has a specific optical property so that, when incidentlight is provided to the cell, emission light is obtained by changing anamplitude and a phase of the incident light in accordance with thespecific amplitude and the specific phase defined in the cell.
 2. Theoptical element as set forth in claim 1, wherein each cell has anamplitude-modulating part provided with transmittance corresponding to aspecific amplitude.
 3. The optical element as set forth in claim 1,wherein each cell has an amplitude-modulating part provided withreflectivity corresponding to a specific amplitude.
 4. The opticalelement as set forth in claim 1, wherein each cell has anamplitude-modulating part provided with an effective area correspondingto a specific amplitude.
 5. The optical element as set forth in claim 1,wherein each cell has a phase-modulating part provided with a refractiveindex corresponding to a specific phase.
 6. The optical element as setforth in claim 1, wherein each cell has a phase-modulating part providedwith an optical path length corresponding to a specific phase.
 7. Theoptical element as set forth in claim 1, wherein each cell has a concavepart formed by hollowing a part provided with an area corresponding to aspecific amplitude by a depth corresponding to a specific phase.
 8. Theoptical element as set forth in claim 7, wherein a surface where theconcave part of each cell is formed serves as a reflecting surface, andincident light provided to the cell is reflected by the reflectingsurface and thereby turns into emission light.
 9. The optical element asset forth in claim 7, wherein each cell includes a main body layerhaving a concave part and a protective layer with which a surface wherethe concave part of the main body layer is formed is covered, and the main body layer and the protective layer are made of materials differentfrom each other.
 10. The optical element as set forth in claim 9,wherein the main body layer and the protective layer are made oftransparent materials different in a refractive index from each other,and incident light provided to the cell passes through the main bodylayer and the protective layer and thereby turns into emission light.11. The optical element as set forth in claim 9, wherein a boundarybetween the main body layer and the protective layer forms a reflectingsurface, and incident light provided to the cell is reflected by thereflecting surface and thereby turns into emission light.
 12. Theoptical element as set forth in claim 1, wherein each cell has a convexpart formed by protruding a part provided with an area corresponding toa specific amplitude by a height corresponding to a specific phase. 13.The optical element as set forth in claim 12, wherein a surface wherethe convex part of each cell is formed serves as a reflecting surface,and incident light provided to the cell is reflected by the reflectingsurface and thereby turns into emission light.
 14. The optical elementas set forth in claim 12, wherein each cell includes a main body layer aconvex part and a protective layer with which a surface where the convexpart of the main body layer is formed is covered, and the main bodylayer and the protective layer are made of materials different from eachother.
 15. The optical element as set forth in claim 14, wherein themain body layer and the protective layer are made of transparentmaterials different in a refractive index from each other, and incidentlight provided to the cell passes through the main body layer and theprotective layer and thereby turns into emission light.
 16. The opticalelement as set forth in claim 14, wherein a boundary between the mainbody layer and the protective layer forms a reflecting surface, andincident light provided to the cell is reflected by the reflectingsurface and thereby turns into emission light.
 17. The optical elementas set forth in claim 1, wherein each cell is arrangedone-dimensionally.
 18. The optical element as set forth in claim 1,wherein each cell is arranged two-dimensionally.
 19. The optical elementas set forth in claim 18, wherein a longitudinal pitch of each cell anda lateral pitch of each cell are arranged so as to be an equal pitch.20. The optical element as set forth in claim 1, wherein a complexamplitude distribution of object light from an object image is recordedso that the object image is reconstructed when observed from apredetermined viewing point so as to be usable as a hologram.
 21. Amethod for manufacturing an optical element where a predetermined objectimage is recorded, the method comprising: a cell defining step ofdefining a set of a plurality of three-dimensional virtual cells; arepresentative-point defining step of defining a representative pointfor each virtual cell; an object image defining step of defining anobject image to be recorded; an amplitude phase defining step ofdefining a specific amplitude and a specific phase in each virtual cellby calculating a complex amplitude at a position of each representativepoint of object light emitted from the object image; and a physical cellforming step of replacing each virtual cell with a real physical celland forming an optical element that consists of a set ofthree-dimensional physical cells; wherein, at the physical cell formingstep, when predetermined incident light is given to each physical cell,replacement is carried out by each physical cell having a specificoptical property so as to obtain emission light that has changed anamplitude and a phase of the incident light in accordance with aspecific amplitude and a specific phase defined in the virtual cellcorresponding to the physical cell.
 22. The manufacturing method for theoptical element as set forth in claim 21, wherein, at the cell definingstep, a cell set is defined by arranging block-like virtual cellsone-dimensionally.
 23. The manufacturing method for the optical elementas set forth in claim 21, wherein, at the cell defining step, a cell setis defined by arranging block-like virtual cells two-dimensionally. 24.The manufacturing method for the optical element as set forth in claim21, wherein, at the amplitude phase defining step, a plurality of pointlight sources are defined on the object image, and object light of aspherical wave having a predetermined amplitude and a predeterminedphase is regarded as being emitted from each point light source, and atotaled complex amplitude of the object light from the point lightsources at a position of each representative point is calculated at apredetermined standard time.
 25. The manufacturing method for theoptical element as set forth in claim 24, wherein K point light sourcesthat emit object light whose wavelength is λ are defined on the objectimage, and if an amplitude of object light emitted from a k-th pointlight source O(k) (k=1 to K) is represented as Ak, and a phase thereofis represented as θ k, and a distance between a predeterminedrepresentative point P and the k-th point light source O(k) isrepresented as rk, a totaled complex amplitude of the object light fromthe K point light sources at the predetermined representative point P iscalculated as follows: Σ_((k=1,K))(Ak/rk·cos (θk+2 πrk/λ) +iAk/rk·sin(θk±2 πrk/λ)).
 26. The manufacturing method for the optical element asset forth in claim 21, wherein, at the physical cell forming step, eachvirtual cell is replaced with a physical cell having a concave partformed by hollowing a part provided with an area corresponding to aspecific amplitude by a depth corresponding to a specific phase.
 27. Themanufacturing method for the optical element as set forth in claim 26,wherein: a refractive index of a material filled in the concave part ofthe physical cell is represented as n1, a refractive index of anothermaterial in contact with the material n1 is represented as n2, awavelength of object light is represented as λ, a maximum depth dmax ofthe concave part is set to be dmax=λ/|n1-n2|, a depth d corresponding toa specific phase θ is determined by the expression d=λ·θ/2(n1-n2)π whenn1>n2, and is determined by the expression d=dmax −λ·θ/2(n2-n1)π whenn1<n2, and an object image is reconstructed by transmission light thathas passed through the concave part.
 28. The manufacturing method forthe optical element as set forth in claim 26, wherein: a refractiveindex of a material filled in the concave part of the physical cell isrepresented as n, a wavelength of object light is represented as λ, amaximum depth of the concave part is set to be dmax =λ/2n, a depth dcorresponding to the specific phase θ is determined by the expressiond=λ·θ/4nπ, and an object image is reconstructed by reflected light thathas been reflected by the boundary of the concave part.
 29. Themanufacturing method for the optical element as set forth in claim 26,wherein α kinds of a plurality of areas are defined as areascorresponding to a specific amplitude, β kinds of a plurality of depthsare defined as depths corresponding to a specific phase so as to prepareα×β kinds of physical cells in total, and each virtual cell is replacedwith a physical cell closest in a necessary optical property among saidphysical cells.
 30. The manufacturing method for the optical element asset forth in claim 21, wherein, at the physical cell forming step, eachvirtual cell is replaced with a physical cell having a convex partformed by protruding a part provided with an area corresponding to aspecific amplitude by a height corresponding to a specific phase. 31.The manufacturing method for the optical element as set forth in claim30, wherein: a refractive index of a material that constitutes theconvex part is represented as n1, a refractive index of another materialin contact with the material n1 is represented as n2, a wavelength ofobject light is represented as λ, a maximum height dmax of the convexpart is set to be dmax=λ/|n1-n2|, a height d corresponding to a specificphase θ is determined by the expression d=λ·θ/2(n1-n2)π when n1>n2, andis determined by the expression d=dmax −λ·θ/2(n2-n1)π when n1<n2, and anobject image is reconstructed by transmission light that has passedthrough the convex part.
 32. The manufacturing method for the opticalelement as set forth in claim 30, wherein: a refractive index of amaterial that constitutes the convex part is represented as n, awavelength of object light is represented as λ, a maximum height dmax ofthe convex part is set to be dmax=λ/2n, a height d corresponding to thespecific phase θ is determined by the expression d=λ·θ/4nπ, and anobject image is reconstructed by reflected light that has been reflectedby the boundary of the convex part.
 33. The manufacturing method for theoptical element as set forth in claim 30, wherein α kinds of a pluralityof areas are defined as areas corresponding to a specific amplitude, βkinds of a plurality of heights are defined as heights corresponding toa specific phase so as to prepare α×β kinds of physical cells in total,and each virtual cell is replaced with a physical cell closest in anecessary optical property among said physical cells.
 34. Themanufacturing method for the optical element as set forth in claim 21,further comprising a phase-correcting step of correcting the specificphase defined for each virtual cell in consideration of a direction ofillumination light projected when reconstructed.
 35. The manufacturingmethod for the optical element as set forth in claim 21, furthercomprising a phase-correcting step of correcting the specific phasedefined for each virtual cell in consideration of a position of aviewing point when reconstructed.
 36. The manufacturing method for theoptical element as set forth in claim 21, wherein: at the cell definingstep, a cell set of virtual cells arranged on a two-dimensional matrixis defined by arranging the virtual cells horizontally and vertically,at the amplitude phase defining step, a plurality of M point lightsource rows that are each extended in a horizontal direction and aremutually disposed in a vertical direction are defined on an objectimage, and M groups in total are defined by defining virtual cells thatbelong to a plurality of rows contiguous in the vertical direction inthe two-dimensional matrix as one group, the M point light source rowsand the M groups are caused to correspond to each other in accordancewith an arrangement order relative to the vertical direction, and atotaled complex amplitude at a position of each representative point iscalculated on a supposition that object light emitted from a point lightsource in an m-th point light source row (m=1 to M) reaches only virtualcells that belongs to an m-th group.